Application of Enhanced Hadamard Error Correcting Code in Video-Watermarking and His Comparison to Reed-Solomon Code

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

Application of Enhanced Hadamard Error Correcting Code in Video-Watermarking and his comparison to Reed-Solomon Code.

Andrzej Dziech1, Jakob Wassermann2, *

1 Dept. of Telecommunication, AGH University of Science and Technology, 30-059 Krakow, Poland 2 Dept. of Electronics and Telecommunications University of Applied Sciences Technikum Wien, 1200 Wien Austria

Abstract. Error Correcting Codes are playing a very important role in Video Watermarking technology. Because of very high compression rate (about 1:200) normally the watermarks can barely survive such massive attacks, despite very sophisticated embedding strategies. It can only work with a sufficient error correcting code method. In this paper, the authors compare the new developed Enhanced Hadamard Error Correcting Code (EHC) with well known Reed-Solomon Code regarding its ability to preserve watermarks in the embedded video. The main idea of this new developed multidimensional Enhanced Hadamard Error Correcting Code is to map the 2D basis images into a collection of one-dimensional rows and to apply a 1D Hadamard decoding procedure on them. After this, the image is reassembled, and the 2D decoding procedure can be applied more efficiently. With this approach, it is possible to overcome the theoretical limit of error correcting capability of (d-1)/2 bits, where d is a Hamming distance. Even better results could be achieved by expanding the 2D EHC to 3D. To prove the efficiency and practicability of this new Enhanced Hadamard Code, the method was applied to a video Watermarking Coding Scheme. The Video Watermarking Embedding procedure decomposes the initial video trough multi-Level Interframe Wavelet Transform. The low pass filtered part of the video stream is used for embedding the watermarks, which are protected respectively by Enhanced Hadamard or Reed-Solomon Correcting Code. The experimental results show that EHC performs much better than RS Code and seems to be very robust against strong MPEG compression.

1 Introduction strong prove of its effectiveness. The reason for selecting Video Watermarking lies in strong compression ratio, Many applications in telecommunication technologies normally factors greater than 1:200, which are applied to are using Hadamard Error Correcting Code. Plotkin [1] the video sequences. For example, an uncompressed was the first who discovered in 1960 error correcting HDTV video stream has a data rate of 1.2Gbit/s and for capabilities of Hadamard matrices. Bose, Shrikhande[2] distribution reason, it must be compressed to 6Mbit/s. and Peterson [3] also have made important contributions. For embedded watermarks, it is a big challenge to sur- Levenshstein [4] was the first who introduced an algo- vive such strong compression ratio. Error correcting rithm for constructing a Hadamard Error Correcting code plays a decisive role in surviving of the embedded Code. The most famous application of Hadamard Error Watermarks. Correcting Code was the NASA space mission in 1969 This paper has followed the structure: In Chapter 2 con- of Mariner and Voyager spacecrafts. Thanks to the pow- tains the introduction to the enhanced Hadamard Error erful error correcting capability of this code it was possi- Correcting Code and its error correcting capabilities. ble to decode properly high-quality pictures of Mars, In Chapter 3, the authors explain the Video Water- Jupiter, Saturn, and Uranus [5]. marking Scheme and the Chapter 4 presents the results In this paper we introduced a new type of multidimen- and discussion. sional Hadamard Code, we called it Enhanced Hadamard Error Correcting Code (EHC). It can overcome the limit of error correcting capability of n/2-1 bits of standard 2 Enhanced Hadamard Error Correcting Hadamard Code, where the codeword length and the Code Hamming distance d have the same value n. The applica- In this chapter, we will give an overview of one- tion of this Code in Video Watermarking gives also a dimensional and two-dimensional Hadamard Code. Then

* Corresponding author: [email protected]

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

the authors explain the enhanced version. that position gives us the ultimate information of the message (010). In the case of one error, the third component of the 2.1 One-Dimensional Hadamard Code spectrum vector d still remains the highest one. In the case of a corrupted codeword c=[-1 1 -1 -1 1 1 -1 -1], the The Hadamard code of n-bit is a non-linear code, which Hadamard spectrum vector delivers: is generated by rows of a n*n Hadamard Matrix Hn. It d 1 1 1 1 1 1 1 1 H 8 can encode k=log2(n) messages and is denoted as (n,k). d 2 2 6 2 2 2 2 2 The Hamming distance is and it can correct 1 n/2, n/2- The third component is still the highest one, so the errors. In the case of n=8 we obtain the following ma- message can be decoded. trix: In the case of two errors, it is already impossible to decode the message unambiguously. C1 1 1 1 1 1 1 1 S D T What is interesting about Hadamard Code is that in the D1 1 1 1 1 1 1 1T (1) D T case of seven and eight errors it is possible again to 1 1 1 1 1 1 1 1 D T decode the codewords. In case of eight errors, our code- D1 1 1 1 1 1 1 1 T

H8 D T word 1 1 1 1 1 1 1 1 D T c=[-1- 1 1 1 -1 -1 1 1] D1 1 1 1 1 1 1 1 T D T is completely corrupted. In this case, the absolute value D1 1 1 1 1 1 1 1 T D T E1 1 1 1 1 1 1 1U of the third component of the Hadamard spectrum is the highest one, and it has a negative sign. A negative sign

The code words are the rows of this Matrix H8. In Table means that the decoded code word must be inverted. 1 the Code Book of the linear Code (8,3) is depicted. The Hamming distance of this code is h=4. d 1 1 1 1 1 1 1 1 H8 d 0 0 8 0 0 0 0 0 In the case of seven errors, we have exactly the same Message Code Words situation as with one error, however, with one small 0 0 0 1 1 1 1 1 1 1 1 difference: the third component has a negative sign, what 0 0 1 1 -1 1 -1 1 -1 1 -1 means the decoded word must be inverted. 0 1 0 1 1 -1 -1 1 1 -1 -1 The following figure shows the error correcting capability of an 8 bit Hadamard code. 0 1 1 1 -1 -1 1 1 -1 -1 1 1 0 0 1 1 1 1 -1 -1 -1 -1 1 0 1 1 -1 1 -1 -1 1 -1 1 1 1 0 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 -1 1 1 -1

Table 1. Code Book of Hadamard Code (8,3)

The decoding procedure is based on Hadamard Spectrum. The spectral component with the highest value determines the decoding message. The received code word is used to build the Hadamard spectrum vector, which enables to determine the corresponding Fig. 1. Error Correcting Capability of 8 Bit Hadamard message. The spectrum vector d is calculated by Code multiplying the code vector c by the Hadamard Matrix H8 . 4 The 8 bit Hadamard code can correct 1,7 and 8-bit errors d c H 8 (2) regardless where they occur within the code words. Supposed we received the code word: Generally, we can say that n bit Hadamard code can c 1 1 1 1 1 1 1 1 correct totally n/2-1 types of errors. The number of error bits occurring in the range According to the Eq.(2), the decoded Hadamard F n V F3 V Spectrum vector is: from G1,, 1W to G n 1,..., nW H 4 X H4 X d 1 1 1 1 1 1 1 1 H8 d 0 0 8 0 0 0 0 0 2.2 Two-Dimensional Hadamard Error Correc- The third component of the vector d has the highest ting Code value in the spectrum; all others are zeroes, d(3)=8, d(i)=0 for i=1,..8 and i≠3. It implicates that the code The 2D Hadamard Error Correcting Code uses so-called word at the position i=3 was received. The codebook at

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

basis images instead of Hadamard vectors. The basis fact, identification of the basis image trough its spectral images functions are orthogonal to each other, and they coefficient, can be utilized to construct error-correcting can be generated from the Hadamard matrix by multipli- code. The codewords are the pattern of basis images, and cation of columns and rows. Generally, we can write they can be decoded unambiguously by detecting the

Aml Hn(:,l)*Hn(m,:) (3) highest absolute coefficient value inside of 2D Hada- In case of 4x4 Hadamard matrix mard Spectrum according to Eq.(4). C1 1 1 1 S Message Basis Matrix Pulse Stream D T Image Element (code word) D1 1 1 1T H 0000 C11 0000000000000000 4 D T D1 1 1 1T D T E1 1 1 1 U 0001 C12 0101010101010101 We can calculate the complete set of 16 such basis images. 0010 C13 0000000011111111

0011 C14 0000111111110000

0100 C21 0000111100001111

0101 C22 01011010010111010

0110 C23 0011110000111100

Fig. 2. Basis Images of 2D Hadamard Transform (4x4)

0111 C24 01101001101101001 For instance, the pattern A31 is generated by Eq.(1) and has the numerical presentation

C 1 S C 1 1 1 1 S 1000 C31 0011001100110011 D T D T D 1 T D 1 1 1 1 T A 4 1 1 1 1 31 D T D T D 1T D 1 1 1 1T 1001 C32 0101010110101010 D T D T E1U E1 1 1 1U

It can be visualized as 1010 C33 0011001111001100

1011 C34 0011110011000011

1100 C41 0110011001100110

Fig. 3. Basis Image A31. The “1” is interpreted as 255 (White) and “-1” as 0 (Black) 1101 C42 0101101010100101 The 2D Hadamard Spectrum of such basis images, which is denoted by C, delivers a matrix where only one coefficient differs from zero. It represents a 2D spectrum 1110 C43 0110011010011001 of the corresponding basis image. For example, the Hadamard spectrum matrix of the pattern A31 is 1111 C44 0110100110010110 C S D 0 0 0 0T D 0 0 0 0T T C H4 A31 H4 D T (4) D16 0 0 0T D T Table 2 : 2D Code Book constructed E 0 0 0 0U from Basic Images

The component C31=16 and all others are zero. This

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

To apply the basic images as codewords, we have to map To show the functionality of this method we consider their two-dimensional structure into one-dimensional the basis images A71 of 8x8 2D Hadamard Transform. pulse stream which will be denoted by the codeword. In This basic image (Fig.5) can be derived from Eq.(3). Table, 2 such 2D Hadamard codebook is depicted.

In case that the basis image A31 is corrupted by some perturbation and looks like it depicted in Figure 4 C S D 1 1 1 1 1 1 1 1 T D 1 1 1 1 1 1 1 1 T D T D 1 1 1 1 1 1 1 1T D1 1 1 1 1 1 1 1T 4 A71 H8 (:,1) H8 (7,:) D T D1 1 1 1 1 1 1 1T D1 1 1 1 1 1 1 1T D T D 1 1 1 1 1 1 1 1 T D T E 1 1 1 1 1 1 1 1 U Fig. 4. Corrupted Basic Image A31

It is still possible to recover the original pattern completely. To understand this, let us consider this Fig. 5. Basic Image A71 of 2D Hadamard Transform corrupted Basic Image: (8x8) and its visualization. “1” is interpreted as white (255), “-1” as black (0) C S D 1 1 1 1 T ~ D 1 1 1 1 T A This image is now corrupted by noise (Fig.6). The 31 D T D 1 1 1 1T corresponding error matrix contains 17 errors. According D T E 1 1 1 1U to the consideration from chapter 2.1, it is not possible to recover this pattern because the number of errors exceeds the limit of n/2-1=15. The Hadamard Spectrum we obtain from

C S D 2 2 2 2 T ~ D 6 2 6 2T (6) C H A H T 31 D T D 10 2 6 2T D T E 2 2 2 2 U

the absolute value of │C31│=10 and it still stays the highest one between the other spectral coefficients of Fig. 6. Original Basis Pattern A71, Error Mask, and the matrix C, hence the corresponding message word could Corrupted Pattern be read out from the code book depicted in Table 2. It is “1000” (see the row for coefficient C31). The functionality of the enhanced Hadamard decoding procedure is depicted in Figure 7. The total number of errors that can be corrected is n/2-1 and correspond completely to the one-dimensional case. The simple enlargement from 1D to 2D doesn’t bring any improvement. To overcome this limit, a new enhance Hadamard decoding procedure for 2D and 3D Hadamard Code is introduced.

2.3 Enhanced 2D Hadamard Error Correcting Code

The enhanced 2D Hadamard Code makes it possible to correct more errors as with the standard Hadamard method. With this approach is possible to overcome the theoretical limit of error correcting capability of n/2-1 errors. The basic idea is to map the 2D basis images into a collection of one-dimensional rows and applying them 1D decoding procedure. After this, the image is reas- A B C D E sembled, and the 2D decoding procedure (Eq.(4)) can be applied more efficiently. Fig. 7. Enhanced Hadamard Decoding Procedure on Error Mask and on Corrupted Basis Image

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

The steps of the algorithm could be described as 2.4 Enhanced 3D Hadamard Error Correcting followes: Code

The corrupted basis image (A) is separated into its The performance of Enhanced Hadamard Code can be rows (B). improved by diluting it to three dimensions. Instead of using basic images, we can use basic cubes for gene- On each row is applied 1D Hadamard decoding pro- rating a code book. cedure. Rows which contain only one error are de- A Hadamard cube is a basis image expanded in the third coded error free (because of each row has the length dimension by multiplying the pattern with Hadamard of n=8). Rows No. 6 and No. 8 are now without any vectors. 4 (7) errors (C). Dmlk Aml Hk (:) where the basis image is represented by Aml and Hk(:) is Reassemble the pattern again (D). The renewed pat- the k Hadamard vector. For example the pattern A41 tern contains now fewer errors as before, namely 15. C S D1 1 1 1T Apply the 2D Hadamard decoding procedure accord- D1 1 1 1T A ing to Eq.(4). The result will be error free pattern (E). 41 D T D1 1 1 1T D T We simulated the error correcting performances of the E1 1 1 1U enhanced and standard Hadamard Error Correcting and the Hadamard vector H2 1 1 1 1 generates Codes with the codewords of the length n=64. The the cube D results are depicted in Fig. 8. On the x-axis, we have the 412 number of bit errors, on the y-axis the number of corrected codewords in percentage. The enhanced Hadamard Code is depicted with a continuous line and standard Hadamard with dashed line. As described in chapter 2.1 the standard Hadamard Error Correcting Code has the following features: It can correct 100% of all corrupted codewords of the length n if the number of error bits occurring in the range [1,.., n/4-1] to [3n/4+1,…,n]. In case n=64 we can see, that standard Hadamard Code corrects all errors if their number is between 1 and 15 and between 49 and 64. In the case of Enhanced Hadamard Correcting Code, we can correct Fig. 9. Hadamard Cube D412 beyond these limits. For example, in the case of 16 errors, we correct 92% of all possible error pattern inside The decoding procedure and the corresponding error the codeword. In the case of 17 errors, it is still 83% of correction work similar to the correcting procedure all error pattern that can be corrected. If we have 48 described in Chapter 2.3. Before it can be applied the errors, in the case of Standard Hadamard Code no errors cube is resolved from the front side in separate layers. could be corrected on the contrary to the Enhanced On each layer, the enhanced 2D Hadamard decoding Hadamard Code. It can correct 92% of all error pattern. procedure is applied. The Performance of the 3D Hadamard Code was simulated and compared with the Standandard Hadamard Code of the length n=512.The Cubes have the dimension 8*8*8. The results are depicted in Figure 10.

Fig. 8. Comparison of Error Correcting Capabilities of Stand- ard Hadamard (dashed line) with 8x8 2D Enhanced Hadamard Code

Fig. 10. Comparison of Error Correcting Capabilities of Sta- nard Hadamard (a) with 3D Enhanced Hadamard Code (b).

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

3 Application of Enhanced Hadamard Code in Watermarking Technology Fig. 12. Watermarking Decoding Process Digital Watermarking is a very prospective new After the selection of the proper DCT coefficients, the technology, that offers a huge number of new inverse QIM (IQIM) is applied. It delivers the decoded applications [6]. Especially the challenge to protect intellectual properties of multimedia data against illegal code words (pulse stream). Through the help of En- usage or tempering can be solved by watermarking hanced Hadamard Error Correcting Code, the original

technologies [7]. One of the important components is an watermark is extracted. error correcting code. Especially when watermarked video sequences undergo a very hard compression the 3.1.1 Multi-Level DWT error correcting code used in the watermarking scheme plays a decisive role in surviving of watermarks[8]. For As mentioned above a multi-Level Interframe DWT this reasons, we choose these techniques to demonstrate with Haar Wavelet was used to deliver a low pass fil- the efficiency of Enhanced Hadamard Error Correcting tered video. The Fig.13 illustrates the operating principle Code (EHC). To underline the performance of EHC, it of this transform. In the first level, the two consecutive was compared with the well known Reed-Solomon Code frames are averaged. In the second level, the frames [9,10] used in the same watermarking scheme. from level one are averaged and so forth. In this watermarking schemes, we used DWT levels from 12 till 16.

3.1 Proposed Watermarking Scheme The proposed watermarking scheme works in the spectral domain and uses an Interframe Discrete Wavelet Transform (DWT) [11] of video sequences and an In- traframe Discrete Cosine Transform (DCT) for embedding procedure [12,13]. In the Fig. 11, the whole encoding process is illustrated. The raw format of the lumi- nance channel of the original video stream is decom- posed by multi-level Interframe DWT with Haar Wave- let. This low pass filtered part of the video stream undergoes a block-wise DCT Transform. From DCT spectrum, special coefficients are selected and used for embedding procedure with 2D Hadamard coded watermarks. The embedding procedure itself is realized through QIM (Quadrature Index Modulation) techniques [14]. Fig. 13. Multi-Level Interframe DWT. At the first level, the two consecutive frames are averaged. At level two the consecutive frames from level one are averaged and so forth.

3.1.2 Selection of Embedded Coefficients Fig. 11. Watermarking Encoding Process To realize the embedding procedure, some coefficients from the DCT spectrum of DWT filtered video The decoder procedure is depicted in Fig.12. At the sequence must be selected. The Fig.14 shows which beginning of the decoding procedure, the embedded coefficients are qualified for watermarking. These are video sequence undergoes the same multi-level Inter- mostly from the yellow area. frame DWT and Intraframe DCT transforms as on the encoder side.

MATEC Web of Conferences 125, 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

The embedded video sequence was compressed with different compression ratios. In the case of compression to 5 Mbit/s, which correspond to a compression ratio of 1:240 it is still possible to extract all watermarks error free. The quality comparison between originally compressed video and embedded and compressed shows, that there is only slightly difference. The SSIM index Video is in this case 98%.

Fig. 14. Coefficients of DCT Spectrum which fits for embedding

3.2 Investigation with 3D Enhanced Hadamard Error Correcting Code

The investigation was done with HDTV video sequence with the resolution of 1080x1920 and 25fps. The video was captured with an AVCHD Camera. The watermarking processing was performed only for the lumi- nance channel (after converting RGB into YCrCb color space) because it is more robust against distortions than Table . Results for 3D Enhanced Hadamard Code any other channels. It was investigated how many embedded watermark bits survive compression attacks without causing significant impairments. The degrada- tion of the watermarked output video was measured with 3.3 Comparison of 3D Enhanced Hadamard with SSIM (Structural Similarity) index. SSIM is based on the Reed-Solomon Code human eye perception and so the expressiveness about In order to show the performance of Enhanced Hada- distortion is better than in the traditional methods like mard Code, a comparison between EHC and well known PSNR (Peak Signal to Noise Ratio) or MSE (Mean Reed-Solomon Code was carried out. Reed-Solomon Square Error) [15]. Code is well known as an error correcting code and it It was chosen the Enhanced 3D Hadamard Code of the has a plenty of practical implementations for example in size of 8x8x8, which means the code word length of 512 consumer electronics like CD, DVD, Blu-Rays, QR- bits. This implies the message code length of 8 bit Code or in data transmission. (log2(n) messages). The DCT block size was 8x8 and from each block were selected 16 coefficients. With To make the Reed-Solomon Code comparable to En- these, information is easy to calculate the total number of hanced Hadamard Code we have to select two parame- embedded watermark bits for each frame. ters: the length of the symbol and the redundancy. The H 4W M 192041080 9 symbol length (block length) is equal to the message of 9 E 4 4C 4 416 9112 Bit/Frame B2 W 82 512 bit. The 3D Enhance Hadamard Code has a codebook, where to every message of 9 bit a cube is assigned with Where H is, the height and W is the width of the codeword length of 512 bits. The Reed-Solomon Code frame. The letter B denotes the block size of DCT trans- has a codebook, where for each message of 9 bit a string form; the letter M is the message code length; the letter of 4599 bits (512 Symbols, each symbol is 9 bit long) is W represents the code word length of the 3D Hadamard assigned. The redundancy of Reed-Solomon Code was Code and the letter C is the number of selected spectral selected in such a way, that the number of correctable coefficients. symbols should approximately correspond to the number In Table , the results of capacity and robustness of correctable bits of Hadamard Code, which is n/2. So measurements are presented. The compression attacks we get an RS Code of [511, 255] with a codeword length were done by H.264 codec with different compression of n=511 symbols and the message of k=255 symbols, ratios. Because the method works in the raw video, the where a symbol is 9 bit long. original data rate is 1.2 Gbit/s. As a watermark was used The comparison of the performance of both codes is a chessboard pattern of the size of 30x30 Pixel. documented in Table . At the data rate of 5Mbit/s, The watermarks were inserted successively into the which correspond to the compression ratio of 1:240, the frames. The Delta QIM gave the width of the quantiza- EHC Code can still recover the whole watermark with- tion steps and was tuned to value 11. Generally, the out errors. In contrary the RS Code shows a recovered Delta value determines the noise distortion in the host watermark with 17% errors. video.

7 125 MATEC Web of Conferences , 05007 (2017) DOI: 10.1051/matecconf/201712505007 CSCC 2017

At the data rate of 3Mbit/s, the performance advantage of EHC is even more visible. EHC Watermark has an error of 1,7%. In contrary the RS Watermark is barely visible and has an error of 27,6%. References Data EHC Err. Reed- Error Rate % Salomon % [1] PLOTKIN,M.: Binary Code with specified minimum dis- 5 Mbit/s tance, IRE Transactions, IT-6:445-450, 1960 0 17,5 [2] BOSE, R.C., SHRIKHANDE, S.S.: A note on the result in the theory of code construction. Inf. And Control 2, 183-194 4 Mbit/s (1965) [3] PETERSON, W.W.: Error correcting codes. The M.I.T. 1,7 27,6 Press, Massachusetts Institute of Technology & J.Wiley & Sons, New York 1961 3 Mbit/s [4] LEVENSHTEIN, V.I.: Application of Hadamard matrices to 6,8 35,3 a problem in coding. Problems of Cybernatics, 5, 166- 184, 1964 [5] Combinatoric in Space, The Mariner 9 Telemetry System, 2 Mbit/s http://www.math.cuden.edu/~wcherowi/courses/m6409/mar iner9talk.pdf 41,2 40,8 [6] SWANSON, M.D., K. M. T. A.: Multimedia Data- Embedding and Watermarking Technologies. In: Proceed- Table . Comparison of Enhanced Hadamard with Reed- ing of IEEE 86 (1998), S. 1064-1087 Salomon Code [7] LIN, S. D., S. C.-F.: A Robust DCT-Based Watermarking for Copyright Protection. In: IEEE Transactions on Con- In all these considerations we should take into account, sumer Electronics 46 (2000), S. 415 that concerning the capacity EHC code is superior [8] SWANSON, M.D., K. M. T. A.: Multimedia Data- against RS code because the EHC codeword length is Embedding and Watermarking Technologies. In: Proceed- ing of IEEE 86 (1998), S. 1064-1087 much shorter (512 bits) than an RS codeword (4599 [9] SHU LIN, DANIEL J.COSTELLO, JR.: Error Control bits). Coding, Prentice-Hall, Inc. Englewood Cliffs, New Jersey 07632 (1983) 4 Conclusion [10] MACWILLIAMS, F.J., Sloane, N.J.A.: The theory of error- correcting codes. North Holland, New York, 1977 In this paper a new type of multidimensional Hadamard [11] PIK-WAH CHAN, M. R. L.: A DWT-Based Digital Video Error Correcting Code, we called it Enhanced Hadamard Watermarking Scheme with Error Correcting Code. In: In- formation and Communications SecurityLecture Notes in Error Correcting Code (EHC) was introduced. It has Computer Science 2836 (2003), S. 202-213 remarkable property, it can overcome the limit of n/2-1 [12] ZHAO, D., C. G. L. W.: A Chaos-Based Robust Wavelet- correctable bit errors of a standard Hadamard Code, Domain Watermarking Algorithm. In: Chaos, Solutions where the codeword length and the Hamming distance d and Fractals 22 (2004), S. 792 have the same value n. The application of this Code in [13] I.J.COX,J.KILLIAN,F.L.& VOL.6 PP., T. S.: Secure Spread Video Watermarking gives also a strong prove of its Spectrum Watermarking for Multimedia. In: IEEE Trans- effectiveness. actions on Image Processing 6 (1997), S. 1673-1687 Compared to Reed-Solomon Code the Enhanced Hada- [14] CHEN,B.,W.G.,WORNELL: Quantization Index Modula- mard Code is much more effective. The watermarks of a tion for Digital Watermarking and Information Embed- video, protected by EHC, can survive a very strong ding of Multimedia. In: Journal of VLSI Signal Pro- 27 (2001), S. 7-33 compression attack, in opposite to RS-Code. cessing EHC protected watermarks can be easily recovered [15] HARTUNG,F.&KUTTER, M.: Multimedia Watermarking error-free from a video with a compression ratio of Techniques. In: Proceeding of IEEE 87 (1999), S. 1079- 1:240, which corresponds to a data rate of 5 Mbit/s. 1107 If the same embedding process is using RS Code instead [16] HO ANTONY T.S., SHEN JUN,SOON HIE TAN,KOT ALEX of EHC the error free recovery of the watermarks is not C..: Digital image-in-image watermarking for copyright possible. It has an error of about 17,5% and the content protection of satellite images using the fast Hadamard of a watermark can barely be recognized. transform. In: Geoscience and Remote Sensing Symposi- All these results are very promising, and they show that um 6 (2002), S. 3311 – 3313 the new Enhanced Hadamard Code is very powerful and can be successfully used in video watermarking.

Performed research was supported by National Science Centre, Poland, Amis project number 2015/16/Z/ST7/00559.